The material in this user-friendly text is presented as simply as possible to ensure that students will gain a solid understanding of statistical procedures and analysis. The goal of this book is to demystify and present statistics in a clear, cohesive manner. The student is presented with rules of evidence and the logic behind those rules. The book is divided into three major units: Descriptive Statistics, Inferential Statistics, and Advanced Topics in Inferential Statistics. Every effort has been made to keep the writing as clear as possible and always aimed at the student's life space. Computational procedures are laid out in a step-by-step, programmed format. This is a straightforward presentation of the essentials of statistical analysis emphasizing the constant interaction between statistical techniques and the resarch methodology.

**Preface**

** **

**I. DESCRIPTIVE STATISTICS**

**1. Introduction to Statistics**

Stumbling Blocks to Statistics

A Brief Look at the History of Statistics

Gertrude Cox (1900-1978)

Benefits of a Course in Statistics

General

Fields of Statistics

Summary

Key Terms and Names

Problems

**2. Percentages, Graphs and Measures of Central Tendency**

Percentage Changes-Comparing Increases with Decreases

Graphs

Measures of Central Tendency

Appropriate Use of the Mean

the Median and the Mode

Summary

Key Terms

Problems

Computer Problems

**3. Variability**

Measures of Variability

Graphs and Variability

Questionnaire Percentages

Key Terms

Computer Problems

**4. The Normal Curve and z Scores**

The Normal Curve

z Scores

Carl Friedrich Gauss (1777-1855)

Translating Raw Scores into z Scores

z Score Translation in Practice

Fun with your Calculator

Summary

Key Terms and Names

Problems

**5. z Scores Revisited: T Scores and Other Normal Curve Transformations**

Other Applications of the z Score

The Percentile Table

T Scores

Normal Cure Equivalents

Stanines

Grade-Equivalent Scores: A Note of Caution

The Importance of the z Score

Summary

Key Terms

Problems

**6. Probability**

The Definition of Probability

Blaise Pascal (1623-1662)

Probability and Percentage Areas of the Normal Curve

Combining Probabilities for Independent Events

A Reminder about Logic

Summary

Key Terms

Problems

**II. INFERENTIAL STATISTICS**

**7. Statistics and Parameters**

Generalizing from the Few to the Many

Key Concepts of Inferential Statistics

Techniques of Sampling

Sampling Distributions

Infinite versus Finite Sampling

Galton and the Concept of Error

Back to z

Some Words of Encouragement

Summary

Key Terms

Problems

**8. Parameter Estimates and Hypothesis Testing**

Estimating the Population Standard Deviation

Estimating the Standard Error of the Mean

Estimating the Population of the Mean**: **Interval Estimates and Hypothesis Testing

The t Ratio

The Type 1 Error

Alpha Levels

Effect Size

Interval Estimates**: **No Hypothesis Test Needed

Summary

Key Terms

Problems

Computer Problems

**9. The Fundamentals of Research Methodology**

Research Strategies

Independent and Dependent Variables

The Cause-and-Effect Trap

Theory of Measurement

Research: Experimental versus Post Facto

The Experimental Method: The Case of Cause and Effect

Creating Equivalent Groups**: **The True Experiment

Designing the True Experiment

The Hawthorne Effect

Repeated-Measures Designs with Separate Control Groups

Requirements for the True Experiment

Post Facto-Research

Combination Research

Research Errors

Experimental Errors

Meta-Analysis

Methodology as a Basis for More Sophisticated Techniques

Summary

Key Terms

Problems

**10. The Hypothesis of Difference**

Sampling Distribution of Differences

Estimated Standard Error of Difference

Two-Sample t Test for Independent Samples

Significance

William Sealy Gossett (1876-1937)

Two-Tailed t Table

Alpha Levels and Confidence Level

The Minimum Difference

Outliner

One-Tail t Test

Importance of Having at Least Two Samples

Power

Effect Size

Summary

Key Terms

Problems

Computer Problems

**11. The Hypothesis of Association: Correlation**

Cause and Effect

The Pearson r

Interclass versus Intraclass

Karl Pearon (1857-1936)

Missing Data

Correlation Matrix

The Spearman r s’ 293 An Important Difference between the Correlation Correlation Coefficient and t Test

Summary

Key Terms and Names

Problems

Computer Problems

**12. Analysis of Variance**

Advantages of ANOVA

The Bonferroni Test

Ronald Aylmer, Fisher (1890-1962)

Analyzing the Variance

Applications of ANOVA

The Factorial ANOVA

Eta Square and d

Graphing the Interaction

Summary

Key Terms and Names

Problems

Computer Problems

**13. Nominal Data and the Chi Square**

Chi Square and Independent Samples

Locating the Difference

Chi Square Percentages

Square and z Scores

Chi Square and Dependent Samples

Requirements for Using Chi Square

Summary

Key Terms

Problems

Computer Problems

**III. ADVANCED TOPICS IN INFERENTIAL STATISTICS**

**14. Regression Analysis **

Regression of Y on X

Sir Francis Galton (1822-1911)

Standard Error of Estimate

Multiple R (Linear Regression with More Than Two Variables)

Path Analysis

The Multiple Rand Causation

Partial Correlation

Summary

Key Terms and Names

Computer Problems

**15. Repeated-Measures and Matched-Subjects Designs With Interval Data**

Problem of Correlated or Dependent Samples

Repeated Measures,

Paired t Ratio

Confidence Interval for Paired Differences

Within-Subjects Effect Size

Testing Correlated Experimental Data

Summary

Key Terms

Problems

Computer Problems

**16. Nonparametrics Revisited: The Ordinal Case**

Mann-Whitney U Test for Two Ordinal Distributions with Independent Selection

Kruskal-Wallis H Test for Three or More Ordinal Distributions with Independent Selection

Wicoxon T Test for Two Ordinal Distributions with Correlated Selection

Friedman ANOVA By Ranks for Three or More Ordinal Distributions with Correlated Selection

Advantages and Disadvantages of Nonparametric Tests

Summary

Key Terms

Problems

**17. Tests and Measurements**

Norm and Criterion Referencing**: **Relative Versus Absolute Performance Measure

The Problem of Bias

Test Reliability

Validityand Measurement Theory

Test Validity

Item Analysis

Summary

Key Terms

Problems

Computer Problems

**18. Computers and Statistical Analysis**

Computer Literacy

The Statistical Programs

Ada Lovelace (nee Byron, 1815-1852)

Logic Checkpoints

Answers

Recommended Reading

**19. Research Simulations: Choosing the Correct Statistical Test**

Methodology**: **Research’s Bottom Line

Checklist Questions

Critical Decision Points

Research Simulations**: **From A to Z

The Research Enterprise

A Final Thought**: **The Burden of Proof

**Special Unit: The Binomial Case**

**Special Unit: The Problem of Unequal Variance**

**Appendix A**

** **

**Appendix B**

** **

**Glossary**

** **

**References**

** **

**Answers to Odd-Numbered Items (and Within-Chapter Exercises)**

** **

**Index**

**Statistical Hall of Fame Biographies**

Gertrude Cox-Chapter 1

Carl Gauss-Chapter 4

Blaise Pascal-Chapter 6

William Gossett-Chapter 10

Karl Pearson-Chapter 11

Ronald Fisher-Chapter 12

Sir Francis Galton-Chapter 14

Ada Lovelace-Chapter 18